## Electronic Journal of Statistics

- Electron. J. Statist.
- Volume 10, Number 2 (2016), 3945-3985.

### Change-point detection in the marginal distribution of a linear process

Farid El Ktaibi and B. Gail Ivanoff

#### Abstract

The subject of this paper is the detection of a change in the marginal distribution of a stationary linear process. By considering the marginal distribution, the change-point model can simultaneously incorporate any change in the coefficients and/or the innovations of the linear process. Furthermore, the change point can be random and data dependent. The key is an analysis of the asymptotic behaviour of the sequential empirical process, both with and without a change point. Our results hold under very mild conditions on the existence of any moment of the innovations and a corresponding condition of summability of the coefficients.

#### Article information

**Source**

Electron. J. Statist., Volume 10, Number 2 (2016), 3945-3985.

**Dates**

Received: October 2015

First available in Project Euclid: 13 December 2016

**Permanent link to this document**

https://projecteuclid.org/euclid.ejs/1481598074

**Digital Object Identifier**

doi:10.1214/16-EJS1215

**Mathematical Reviews number (MathSciNet)**

MR3581958

**Zentralblatt MATH identifier**

1353.62095

**Subjects**

Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]

Secondary: 62G10, 62G30, 60F17

**Keywords**

Causal linear process sequential empirical process change-point

#### Citation

El Ktaibi, Farid; Ivanoff, B. Gail. Change-point detection in the marginal distribution of a linear process. Electron. J. Statist. 10 (2016), no. 2, 3945--3985. doi:10.1214/16-EJS1215. https://projecteuclid.org/euclid.ejs/1481598074